# Write a factorial formula for the product of: 1) the first six odd positive integers 2) the first ten odd "+"integers 3) the first n odd positive intg

*print*Print*list*Cite

### 1 Answer

**For any n, the product of the first n odd positive integers is given by**

----------------

`P=((2n)!)/(n!2^n)`

----------------

For example:

1x3x5x7x9x11=`(12!)/(6!2^6)=(12*11*10*9*8*7)/(64)` Notice that all of the even factors cancel leaving 3x11x5x9x7 in the numerator, as required.

The first 10 odd positive integers:

1x3x5x7x9x11x13x15x17x19=`(38!)/(10!2^(10))`

**Sources:**